Abstract
A new scheme to cope with two-stage stochastic optimization problems uses a risk measure as the objective function of the recourse action, where the risk measure is defined as the worst-case expected values over a set of constrained distributions. This paper develops an approach to deal with the case where both the first and second stage objective functions are convex linear-quadratic. It is shown that under a standard set of regularity assumptions, this two-stage quadratic stochastic optimization problem with measures of risk is equivalent to a conic optimization problem that can be solved in polynomial time.
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This research is partially supported by Australian Research Council under Grant DP160102819 and by a Grant from General Research Fund (GRF) of Hong Kong.
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This paper is dedicated to Terry Rockafellar in celebration of his 80th birthday.
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Sun, J., Liao, LZ. & Rodrigues, B. Quadratic two-stage stochastic optimization with coherent measures of risk. Math. Program. 168, 599–613 (2018). https://doi.org/10.1007/s10107-017-1131-x
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DOI: https://doi.org/10.1007/s10107-017-1131-x